%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : MGT026+1 : TPTP v9.3.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.L4PvPGNSIP true
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:24:49 AM UTC 2026
% Result : Theorem 0.41s 0.71s
% Output : Refutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of formulae : 95 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 299 ( 67 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1075 ( 163 ~; 169 |; 22 &; 708 @)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 104 ( 0 ^; 104 !; 0 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
thf(selection_favors_type,type,
selection_favors: $i > $i > $i > $o ).
thf(first_movers_type,type,
first_movers: $i ).
thf(zero_type,type,
zero: $i ).
thf(appear_type,type,
appear: $i > $i > $i ).
thf(subpopulations_type,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(growth_rate_type,type,
growth_rate: $i > $i > $i ).
thf(in_environment_type,type,
in_environment: $i > $i > $o ).
thf(cardinality_at_time_type,type,
cardinality_at_time: $i > $i > $i ).
thf(sk__1_type,type,
sk__1: $i ).
thf(efficient_producers_type,type,
efficient_producers: $i ).
thf(greater_or_equal_type,type,
greater_or_equal: $i > $i > $o ).
thf(sk__type,type,
sk_: $i ).
thf(critical_point_type,type,
critical_point: $i > $i ).
thf(environment_type,type,
environment: $i > $o ).
thf(greater_type,type,
greater: $i > $i > $o ).
thf(subpopulation_type,type,
subpopulation: $i > $i > $i > $o ).
thf(prove_l8,conjecture,
! [E: $i,T: $i] :
( ( ( environment @ E )
& ( in_environment @ E @ T )
& ( greater @ T @ ( critical_point @ E ) ) )
=> ( selection_favors @ efficient_producers @ first_movers @ T ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [E: $i,T: $i] :
( ( ( environment @ E )
& ( in_environment @ E @ T )
& ( greater @ T @ ( critical_point @ E ) ) )
=> ( selection_favors @ efficient_producers @ first_movers @ T ) ),
inference('cnf.neg',[status(esa)],[prove_l8]) ).
thf(zip_derived_cl16,plain,
in_environment @ sk_ @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(mp_subpopulations,axiom,
! [E: $i,T: $i] :
( ( ( environment @ E )
& ( in_environment @ E @ T ) )
=> ( ( subpopulation @ first_movers @ E @ T )
& ( subpopulation @ efficient_producers @ E @ T ) ) ) ).
thf(zip_derived_cl4,plain,
! [X0: $i,X1: $i] :
( ~ ( environment @ X0 )
| ~ ( in_environment @ X0 @ X1 )
| ( subpopulation @ efficient_producers @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[mp_subpopulations]) ).
thf(zip_derived_cl128,plain,
( ( subpopulation @ efficient_producers @ sk_ @ sk__1 )
| ~ ( environment @ sk_ ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl16,zip_derived_cl4]) ).
thf(zip_derived_cl17,plain,
environment @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl136,plain,
subpopulation @ efficient_producers @ sk_ @ sk__1,
inference(demod,[status(thm)],[zip_derived_cl128,zip_derived_cl17]) ).
thf(mp2_favour_members,axiom,
! [E: $i,S1: $i,S2: $i,T: $i] :
( ( ( environment @ E )
& ( subpopulation @ S1 @ E @ T )
& ( subpopulation @ S2 @ E @ T )
& ( greater @ ( cardinality_at_time @ S1 @ T ) @ zero )
& ( ( cardinality_at_time @ S2 @ T )
= zero ) )
=> ( selection_favors @ S1 @ S2 @ T ) ) ).
thf(zip_derived_cl1,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( environment @ X0 )
| ~ ( subpopulation @ X1 @ X0 @ X2 )
| ~ ( subpopulation @ X3 @ X0 @ X2 )
| ~ ( greater @ ( cardinality_at_time @ X1 @ X2 ) @ zero )
| ( ( cardinality_at_time @ X3 @ X2 )
!= zero )
| ( selection_favors @ X1 @ X3 @ X2 ) ),
inference(cnf,[status(esa)],[mp2_favour_members]) ).
thf(zip_derived_cl14,plain,
~ ( selection_favors @ efficient_producers @ first_movers @ sk__1 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl117,plain,
! [X0: $i] :
( ( ( cardinality_at_time @ first_movers @ sk__1 )
!= zero )
| ~ ( greater @ ( cardinality_at_time @ efficient_producers @ sk__1 ) @ zero )
| ~ ( subpopulation @ first_movers @ X0 @ sk__1 )
| ~ ( subpopulation @ efficient_producers @ X0 @ sk__1 )
| ~ ( environment @ X0 ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl1,zip_derived_cl14]) ).
thf(mp_critical_point_after_EP,axiom,
! [E: $i] :
( ( environment @ E )
=> ( greater_or_equal @ ( critical_point @ E ) @ ( appear @ efficient_producers @ E ) ) ) ).
thf(zip_derived_cl6,plain,
! [X0: $i] :
( ( greater_or_equal @ ( critical_point @ X0 ) @ ( appear @ efficient_producers @ X0 ) )
| ~ ( environment @ X0 ) ),
inference(cnf,[status(esa)],[mp_critical_point_after_EP]) ).
thf(mp_greater_or_equal,axiom,
! [X: $i,Y: $i] :
( ( greater_or_equal @ X @ Y )
<=> ( ( greater @ X @ Y )
| ( X = Y ) ) ) ).
thf(zip_derived_cl8,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( greater @ X1 @ X0 )
| ~ ( greater_or_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[mp_greater_or_equal]) ).
thf(zip_derived_cl125,plain,
! [X0: $i] :
( ~ ( environment @ X0 )
| ( greater @ ( critical_point @ X0 ) @ ( appear @ efficient_producers @ X0 ) )
| ( ( critical_point @ X0 )
= ( appear @ efficient_producers @ X0 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl6,zip_derived_cl8]) ).
thf(zip_derived_cl15,plain,
greater @ sk__1 @ ( critical_point @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(mp_greater_transitivity,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( greater @ X @ Y )
& ( greater @ Y @ Z ) )
=> ( greater @ X @ Z ) ) ).
thf(zip_derived_cl7,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( greater @ X0 @ X1 )
| ~ ( greater @ X1 @ X2 )
| ( greater @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[mp_greater_transitivity]) ).
thf(zip_derived_cl139,plain,
! [X0: $i] :
( ~ ( greater @ ( critical_point @ sk_ ) @ X0 )
| ( greater @ sk__1 @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl15,zip_derived_cl7]) ).
thf(zip_derived_cl146,plain,
( ( ( critical_point @ sk_ )
= ( appear @ efficient_producers @ sk_ ) )
| ~ ( environment @ sk_ )
| ( greater @ sk__1 @ ( appear @ efficient_producers @ sk_ ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl125,zip_derived_cl139]) ).
thf(zip_derived_cl17_001,plain,
environment @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl147,plain,
( ( ( critical_point @ sk_ )
= ( appear @ efficient_producers @ sk_ ) )
| ( greater @ sk__1 @ ( appear @ efficient_producers @ sk_ ) ) ),
inference(demod,[status(thm)],[zip_derived_cl146,zip_derived_cl17]) ).
thf(zip_derived_cl16_002,plain,
in_environment @ sk_ @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl9,plain,
! [X0: $i,X1: $i] :
( ( greater_or_equal @ X0 @ X1 )
| ~ ( greater @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[mp_greater_or_equal]) ).
thf(t6,axiom,
! [E: $i,T: $i] :
( ( ( environment @ E )
& ( in_environment @ E @ T )
& ( greater_or_equal @ T @ ( appear @ efficient_producers @ E ) ) )
=> ( greater @ ( cardinality_at_time @ efficient_producers @ T ) @ zero ) ) ).
thf(zip_derived_cl13,plain,
! [X0: $i,X1: $i] :
( ~ ( environment @ X0 )
| ~ ( in_environment @ X0 @ X1 )
| ~ ( greater_or_equal @ X1 @ ( appear @ efficient_producers @ X0 ) )
| ( greater @ ( cardinality_at_time @ efficient_producers @ X1 ) @ zero ) ),
inference(cnf,[status(esa)],[t6]) ).
thf(zip_derived_cl126,plain,
! [X0: $i,X1: $i] :
( ~ ( greater @ X1 @ ( appear @ efficient_producers @ X0 ) )
| ( greater @ ( cardinality_at_time @ efficient_producers @ X1 ) @ zero )
| ~ ( in_environment @ X0 @ X1 )
| ~ ( environment @ X0 ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl9,zip_derived_cl13]) ).
thf(zip_derived_cl133,plain,
( ~ ( environment @ sk_ )
| ( greater @ ( cardinality_at_time @ efficient_producers @ sk__1 ) @ zero )
| ~ ( greater @ sk__1 @ ( appear @ efficient_producers @ sk_ ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl16,zip_derived_cl126]) ).
thf(zip_derived_cl17_003,plain,
environment @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl141,plain,
( ( greater @ ( cardinality_at_time @ efficient_producers @ sk__1 ) @ zero )
| ~ ( greater @ sk__1 @ ( appear @ efficient_producers @ sk_ ) ) ),
inference(demod,[status(thm)],[zip_derived_cl133,zip_derived_cl17]) ).
thf(zip_derived_cl149,plain,
( ( ( critical_point @ sk_ )
= ( appear @ efficient_producers @ sk_ ) )
| ( greater @ ( cardinality_at_time @ efficient_producers @ sk__1 ) @ zero ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl147,zip_derived_cl141]) ).
thf(zip_derived_cl141_004,plain,
( ( greater @ ( cardinality_at_time @ efficient_producers @ sk__1 ) @ zero )
| ~ ( greater @ sk__1 @ ( appear @ efficient_producers @ sk_ ) ) ),
inference(demod,[status(thm)],[zip_derived_cl133,zip_derived_cl17]) ).
thf(zip_derived_cl151,plain,
( ( greater @ ( cardinality_at_time @ efficient_producers @ sk__1 ) @ zero )
| ( greater @ ( cardinality_at_time @ efficient_producers @ sk__1 ) @ zero )
| ~ ( greater @ sk__1 @ ( critical_point @ sk_ ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl149,zip_derived_cl141]) ).
thf(zip_derived_cl15_005,plain,
greater @ sk__1 @ ( critical_point @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl155,plain,
( ( greater @ ( cardinality_at_time @ efficient_producers @ sk__1 ) @ zero )
| ( greater @ ( cardinality_at_time @ efficient_producers @ sk__1 ) @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl151,zip_derived_cl15]) ).
thf(zip_derived_cl156,plain,
greater @ ( cardinality_at_time @ efficient_producers @ sk__1 ) @ zero,
inference(simplify,[status(thm)],[zip_derived_cl155]) ).
thf(zip_derived_cl159,plain,
! [X0: $i] :
( ( ( cardinality_at_time @ first_movers @ sk__1 )
!= zero )
| ~ ( subpopulation @ first_movers @ X0 @ sk__1 )
| ~ ( subpopulation @ efficient_producers @ X0 @ sk__1 )
| ~ ( environment @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl117,zip_derived_cl156]) ).
thf(zip_derived_cl16_006,plain,
in_environment @ sk_ @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(mp_first_movers_exist,axiom,
! [E: $i,T: $i] :
( ( ( environment @ E )
& ( in_environment @ E @ T ) )
=> ( greater_or_equal @ ( cardinality_at_time @ first_movers @ T ) @ zero ) ) ).
thf(zip_derived_cl3,plain,
! [X0: $i,X1: $i] :
( ~ ( environment @ X0 )
| ~ ( in_environment @ X0 @ X1 )
| ( greater_or_equal @ ( cardinality_at_time @ first_movers @ X1 ) @ zero ) ),
inference(cnf,[status(esa)],[mp_first_movers_exist]) ).
thf(zip_derived_cl8_007,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( greater @ X1 @ X0 )
| ~ ( greater_or_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[mp_greater_or_equal]) ).
thf(zip_derived_cl124,plain,
! [X0: $i,X1: $i] :
( ~ ( in_environment @ X0 @ X1 )
| ~ ( environment @ X0 )
| ( greater @ ( cardinality_at_time @ first_movers @ X1 ) @ zero )
| ( ( cardinality_at_time @ first_movers @ X1 )
= zero ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl3,zip_derived_cl8]) ).
thf(zip_derived_cl132,plain,
( ( ( cardinality_at_time @ first_movers @ sk__1 )
= zero )
| ( greater @ ( cardinality_at_time @ first_movers @ sk__1 ) @ zero )
| ~ ( environment @ sk_ ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl16,zip_derived_cl124]) ).
thf(zip_derived_cl17_008,plain,
environment @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl143,plain,
( ( ( cardinality_at_time @ first_movers @ sk__1 )
= zero )
| ( greater @ ( cardinality_at_time @ first_movers @ sk__1 ) @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl132,zip_derived_cl17]) ).
thf(zip_derived_cl16_009,plain,
in_environment @ sk_ @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(mp_non_empty_fm_and_ep,axiom,
! [E: $i,T: $i] :
( ( ( environment @ E )
& ( in_environment @ E @ T )
& ( greater @ ( cardinality_at_time @ first_movers @ T ) @ zero )
& ( greater @ ( cardinality_at_time @ efficient_producers @ T ) @ zero ) )
=> ( subpopulations @ first_movers @ efficient_producers @ E @ T ) ) ).
thf(zip_derived_cl2,plain,
! [X0: $i,X1: $i] :
( ~ ( environment @ X0 )
| ~ ( in_environment @ X0 @ X1 )
| ~ ( greater @ ( cardinality_at_time @ first_movers @ X1 ) @ zero )
| ~ ( greater @ ( cardinality_at_time @ efficient_producers @ X1 ) @ zero )
| ( subpopulations @ first_movers @ efficient_producers @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[mp_non_empty_fm_and_ep]) ).
thf(d1,axiom,
! [E: $i,Tc: $i] :
( ( ( environment @ E )
& ( Tc
= ( critical_point @ E ) ) )
=> ( ~ ( greater @ ( growth_rate @ efficient_producers @ Tc ) @ ( growth_rate @ first_movers @ Tc ) )
& ! [T: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ E @ T )
& ( greater @ T @ Tc ) )
=> ( greater @ ( growth_rate @ efficient_producers @ T ) @ ( growth_rate @ first_movers @ T ) ) ) ) ) ).
thf(zip_derived_cl11,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( environment @ X0 )
| ( X1
!= ( critical_point @ X0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ X2 ) @ ( growth_rate @ first_movers @ X2 ) )
| ~ ( greater @ X2 @ X1 )
| ~ ( subpopulations @ first_movers @ efficient_producers @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[d1]) ).
thf(zip_derived_cl120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( first_movers != first_movers )
| ( efficient_producers != efficient_producers )
| ( X0 != X2 )
| ( X1 != X4 )
| ~ ( greater @ ( cardinality_at_time @ efficient_producers @ X1 ) @ zero )
| ~ ( greater @ ( cardinality_at_time @ first_movers @ X1 ) @ zero )
| ~ ( in_environment @ X0 @ X1 )
| ~ ( environment @ X0 )
| ~ ( greater @ X4 @ X3 )
| ( greater @ ( growth_rate @ efficient_producers @ X4 ) @ ( growth_rate @ first_movers @ X4 ) )
| ( X3
!= ( critical_point @ X2 ) )
| ~ ( environment @ X2 ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl2,zip_derived_cl11]) ).
thf(zip_derived_cl130,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( environment @ X0 )
| ( X2
!= ( critical_point @ X0 ) )
| ( greater @ ( growth_rate @ efficient_producers @ X1 ) @ ( growth_rate @ first_movers @ X1 ) )
| ~ ( greater @ X1 @ X2 )
| ~ ( environment @ sk_ )
| ~ ( greater @ ( cardinality_at_time @ first_movers @ sk__1 ) @ zero )
| ~ ( greater @ ( cardinality_at_time @ efficient_producers @ sk__1 ) @ zero )
| ( sk__1 != X1 )
| ( sk_ != X0 )
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl16,zip_derived_cl120]) ).
thf(zip_derived_cl161,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_ != X0 )
| ( sk__1 != X1 )
| ~ ( greater @ ( cardinality_at_time @ efficient_producers @ sk__1 ) @ zero )
| ~ ( greater @ ( cardinality_at_time @ first_movers @ sk__1 ) @ zero )
| ~ ( environment @ sk_ )
| ~ ( greater @ X1 @ X2 )
| ( greater @ ( growth_rate @ efficient_producers @ X1 ) @ ( growth_rate @ first_movers @ X1 ) )
| ( X2
!= ( critical_point @ X0 ) )
| ~ ( environment @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl130]) ).
thf(zip_derived_cl156_010,plain,
greater @ ( cardinality_at_time @ efficient_producers @ sk__1 ) @ zero,
inference(simplify,[status(thm)],[zip_derived_cl155]) ).
thf(zip_derived_cl17_011,plain,
environment @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl162,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_ != X0 )
| ( sk__1 != X1 )
| ~ ( greater @ ( cardinality_at_time @ first_movers @ sk__1 ) @ zero )
| ~ ( greater @ X1 @ X2 )
| ( greater @ ( growth_rate @ efficient_producers @ X1 ) @ ( growth_rate @ first_movers @ X1 ) )
| ( X2
!= ( critical_point @ X0 ) )
| ~ ( environment @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl161,zip_derived_cl156,zip_derived_cl17]) ).
thf(zip_derived_cl163,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( cardinality_at_time @ first_movers @ sk__1 )
= zero )
| ( sk_ != X0 )
| ( sk__1 != X1 )
| ~ ( greater @ X1 @ X2 )
| ( greater @ ( growth_rate @ efficient_producers @ X1 ) @ ( growth_rate @ first_movers @ X1 ) )
| ( X2
!= ( critical_point @ X0 ) )
| ~ ( environment @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl143,zip_derived_cl162]) ).
thf(zip_derived_cl171,plain,
! [X0: $i,X1: $i] :
( ~ ( environment @ sk_ )
| ( X0
!= ( critical_point @ sk_ ) )
| ( greater @ ( growth_rate @ efficient_producers @ X1 ) @ ( growth_rate @ first_movers @ X1 ) )
| ~ ( greater @ X1 @ X0 )
| ( sk__1 != X1 )
| ( ( cardinality_at_time @ first_movers @ sk__1 )
= zero ) ),
inference(eq_res,[status(thm)],[zip_derived_cl163]) ).
thf(zip_derived_cl17_012,plain,
environment @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl172,plain,
! [X0: $i,X1: $i] :
( ( X0
!= ( critical_point @ sk_ ) )
| ( greater @ ( growth_rate @ efficient_producers @ X1 ) @ ( growth_rate @ first_movers @ X1 ) )
| ~ ( greater @ X1 @ X0 )
| ( sk__1 != X1 )
| ( ( cardinality_at_time @ first_movers @ sk__1 )
= zero ) ),
inference(demod,[status(thm)],[zip_derived_cl171,zip_derived_cl17]) ).
thf(zip_derived_cl174,plain,
! [X0: $i] :
( ( ( cardinality_at_time @ first_movers @ sk__1 )
= zero )
| ~ ( greater @ sk__1 @ X0 )
| ( greater @ ( growth_rate @ efficient_producers @ sk__1 ) @ ( growth_rate @ first_movers @ sk__1 ) )
| ( X0
!= ( critical_point @ sk_ ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl172]) ).
thf(zip_derived_cl175,plain,
( ( greater @ ( growth_rate @ efficient_producers @ sk__1 ) @ ( growth_rate @ first_movers @ sk__1 ) )
| ~ ( greater @ sk__1 @ ( critical_point @ sk_ ) )
| ( ( cardinality_at_time @ first_movers @ sk__1 )
= zero ) ),
inference(eq_res,[status(thm)],[zip_derived_cl174]) ).
thf(zip_derived_cl15_013,plain,
greater @ sk__1 @ ( critical_point @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl176,plain,
( ( greater @ ( growth_rate @ efficient_producers @ sk__1 ) @ ( growth_rate @ first_movers @ sk__1 ) )
| ( ( cardinality_at_time @ first_movers @ sk__1 )
= zero ) ),
inference(demod,[status(thm)],[zip_derived_cl175,zip_derived_cl15]) ).
thf(zip_derived_cl143_014,plain,
( ( ( cardinality_at_time @ first_movers @ sk__1 )
= zero )
| ( greater @ ( cardinality_at_time @ first_movers @ sk__1 ) @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl132,zip_derived_cl17]) ).
thf(zip_derived_cl16_015,plain,
in_environment @ sk_ @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2_016,plain,
! [X0: $i,X1: $i] :
( ~ ( environment @ X0 )
| ~ ( in_environment @ X0 @ X1 )
| ~ ( greater @ ( cardinality_at_time @ first_movers @ X1 ) @ zero )
| ~ ( greater @ ( cardinality_at_time @ efficient_producers @ X1 ) @ zero )
| ( subpopulations @ first_movers @ efficient_producers @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[mp_non_empty_fm_and_ep]) ).
thf(mp1_high_growth_rates,axiom,
! [E: $i,S1: $i,S2: $i,T: $i] :
( ( ( environment @ E )
& ( subpopulations @ S1 @ S2 @ E @ T )
& ( greater @ ( growth_rate @ S2 @ T ) @ ( growth_rate @ S1 @ T ) ) )
=> ( selection_favors @ S2 @ S1 @ T ) ) ).
thf(zip_derived_cl0,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( environment @ X0 )
| ~ ( subpopulations @ X1 @ X2 @ X0 @ X3 )
| ~ ( greater @ ( growth_rate @ X2 @ X3 ) @ ( growth_rate @ X1 @ X3 ) )
| ( selection_favors @ X2 @ X1 @ X3 ) ),
inference(cnf,[status(esa)],[mp1_high_growth_rates]) ).
thf(zip_derived_cl14_017,plain,
~ ( selection_favors @ efficient_producers @ first_movers @ sk__1 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl116,plain,
! [X0: $i] :
( ~ ( greater @ ( growth_rate @ efficient_producers @ sk__1 ) @ ( growth_rate @ first_movers @ sk__1 ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ X0 @ sk__1 )
| ~ ( environment @ X0 ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl0,zip_derived_cl14]) ).
thf(zip_derived_cl123,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( first_movers != first_movers )
| ( efficient_producers != efficient_producers )
| ( X0 != X2 )
| ( X1 != sk__1 )
| ~ ( greater @ ( cardinality_at_time @ efficient_producers @ X1 ) @ zero )
| ~ ( greater @ ( cardinality_at_time @ first_movers @ X1 ) @ zero )
| ~ ( in_environment @ X0 @ X1 )
| ~ ( environment @ X0 )
| ~ ( environment @ X2 )
| ~ ( greater @ ( growth_rate @ efficient_producers @ sk__1 ) @ ( growth_rate @ first_movers @ sk__1 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl2,zip_derived_cl116]) ).
thf(zip_derived_cl131,plain,
! [X0: $i] :
( ~ ( greater @ ( growth_rate @ efficient_producers @ sk__1 ) @ ( growth_rate @ first_movers @ sk__1 ) )
| ~ ( environment @ X0 )
| ~ ( environment @ sk_ )
| ~ ( greater @ ( cardinality_at_time @ first_movers @ sk__1 ) @ zero )
| ~ ( greater @ ( cardinality_at_time @ efficient_producers @ sk__1 ) @ zero )
| ( sk__1 != sk__1 )
| ( sk_ != X0 )
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl16,zip_derived_cl123]) ).
thf(zip_derived_cl164,plain,
! [X0: $i] :
( ( sk_ != X0 )
| ~ ( greater @ ( cardinality_at_time @ efficient_producers @ sk__1 ) @ zero )
| ~ ( greater @ ( cardinality_at_time @ first_movers @ sk__1 ) @ zero )
| ~ ( environment @ sk_ )
| ~ ( environment @ X0 )
| ~ ( greater @ ( growth_rate @ efficient_producers @ sk__1 ) @ ( growth_rate @ first_movers @ sk__1 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl131]) ).
thf(zip_derived_cl156_018,plain,
greater @ ( cardinality_at_time @ efficient_producers @ sk__1 ) @ zero,
inference(simplify,[status(thm)],[zip_derived_cl155]) ).
thf(zip_derived_cl17_019,plain,
environment @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl165,plain,
! [X0: $i] :
( ( sk_ != X0 )
| ~ ( greater @ ( cardinality_at_time @ first_movers @ sk__1 ) @ zero )
| ~ ( environment @ X0 )
| ~ ( greater @ ( growth_rate @ efficient_producers @ sk__1 ) @ ( growth_rate @ first_movers @ sk__1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl164,zip_derived_cl156,zip_derived_cl17]) ).
thf(zip_derived_cl166,plain,
! [X0: $i] :
( ( ( cardinality_at_time @ first_movers @ sk__1 )
= zero )
| ( sk_ != X0 )
| ~ ( environment @ X0 )
| ~ ( greater @ ( growth_rate @ efficient_producers @ sk__1 ) @ ( growth_rate @ first_movers @ sk__1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl143,zip_derived_cl165]) ).
thf(zip_derived_cl178,plain,
! [X0: $i] :
( ( ( cardinality_at_time @ first_movers @ sk__1 )
= zero )
| ( ( cardinality_at_time @ first_movers @ sk__1 )
= zero )
| ( sk_ != X0 )
| ~ ( environment @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl176,zip_derived_cl166]) ).
thf(zip_derived_cl179,plain,
! [X0: $i] :
( ~ ( environment @ X0 )
| ( sk_ != X0 )
| ( ( cardinality_at_time @ first_movers @ sk__1 )
= zero ) ),
inference(simplify,[status(thm)],[zip_derived_cl178]) ).
thf(zip_derived_cl180,plain,
( ( ( cardinality_at_time @ first_movers @ sk__1 )
= zero )
| ~ ( environment @ sk_ ) ),
inference(eq_res,[status(thm)],[zip_derived_cl179]) ).
thf(zip_derived_cl17_020,plain,
environment @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl181,plain,
( ( cardinality_at_time @ first_movers @ sk__1 )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl180,zip_derived_cl17]) ).
thf(zip_derived_cl182,plain,
! [X0: $i] :
( ( zero != zero )
| ~ ( subpopulation @ first_movers @ X0 @ sk__1 )
| ~ ( subpopulation @ efficient_producers @ X0 @ sk__1 )
| ~ ( environment @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl159,zip_derived_cl181]) ).
thf(zip_derived_cl183,plain,
! [X0: $i] :
( ~ ( environment @ X0 )
| ~ ( subpopulation @ efficient_producers @ X0 @ sk__1 )
| ~ ( subpopulation @ first_movers @ X0 @ sk__1 ) ),
inference(simplify,[status(thm)],[zip_derived_cl182]) ).
thf(zip_derived_cl186,plain,
( ~ ( environment @ sk_ )
| ~ ( subpopulation @ first_movers @ sk_ @ sk__1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl136,zip_derived_cl183]) ).
thf(zip_derived_cl17_021,plain,
environment @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl16_022,plain,
in_environment @ sk_ @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl5,plain,
! [X0: $i,X1: $i] :
( ~ ( environment @ X0 )
| ~ ( in_environment @ X0 @ X1 )
| ( subpopulation @ first_movers @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[mp_subpopulations]) ).
thf(zip_derived_cl129,plain,
( ( subpopulation @ first_movers @ sk_ @ sk__1 )
| ~ ( environment @ sk_ ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl16,zip_derived_cl5]) ).
thf(zip_derived_cl17_023,plain,
environment @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl140,plain,
subpopulation @ first_movers @ sk_ @ sk__1,
inference(demod,[status(thm)],[zip_derived_cl129,zip_derived_cl17]) ).
thf(zip_derived_cl187,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl186,zip_derived_cl17,zip_derived_cl140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT026+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.04 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.L4PvPGNSIP true
% 0.11/0.36 % Computer : n026.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 7 12:14:42 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Running portfolio for 300 s
% 0.11/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Number of cores: 8
% 0.11/0.37 % Python version: Python 3.12.3
% 0.11/0.38 % Running in FO mode
% 0.35/0.59 % Total configuration time : 435
% 0.35/0.59 % Estimated wc time : 1092
% 0.35/0.59 % Estimated cpu time (7 cpus) : 156.0
% 0.41/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.41/0.71 % Solved by fo/fo6_bce.sh.
% 0.41/0.71 % BCE start: 18
% 0.41/0.71 % BCE eliminated: 0
% 0.41/0.71 % PE start: 18
% 0.41/0.71 logic: eq
% 0.41/0.71 % PE eliminated: 5
% 0.41/0.71 % done 35 iterations in 0.025s
% 0.41/0.71 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.41/0.71 % SZS output start Refutation
% See solution above
% 0.41/0.71
% 0.41/0.71
% 0.41/0.71 % Terminating...
% 0.41/0.75 % Runner terminated.
% 0.41/0.76 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------